PY211 MIDTERM REVIEW
state 2 characteristics of a probability
2 characteristics of probability: the probability varies between 0 and 1 and can never be negative
how many scores are included to compute the range
2 scores; the largest and the smallest scores in the distribution
on the basis of statistics from the previous 3 years, a maternity ward states that 97% of patients say they are satisfied with their birthing experience. if 100,000 patients gave birth in that maternity ward over the previous 3 years, then how many patients do we expect were not satisfied with their visit
3000 mothers were not satisfied
Would it be most appropriate to use a bar chart or a histogram to summarize the frequency distribution of each of the following? (A) The delay to start a game in minutes (B) The number of students in each of three classrooms (C)The age (in years) that a sample of women first conceived (D) The direction of a person's eye movement (right, left, or center) when he or she is telling a lie
histogram, bar chart, histogram, bar chart
what is the main distinction between variables on an interval scale and those on a ratio scale of measurement?
interval variables do not have a true zero, ratio variables do have a true zero
The following table lists the number of text messages sent per day in a sample of college students and a sample of their parents. Compute the mean, the median, and the mode for the college students' and parents' data.Based on the shape of the distribution for each sample, which measure of central tendency is most appropriate for describing each sample? Explain how describing each sample with only the most appropriate measure might be misleading. College Students: 43,12,14,13,54,7,50,15,21,21 Parents: 24,21,0,12,20,19,21,5,3,10
"(a) College students: mean = 25, median = 18, mode = 21. Parents: mean = 14, median = 18, mode = 21. (b) Because both distributions are skewed, the median would be the appropriate measure of central tendency. This might be misleading, though, because the median indicates that texting was the same between groups (the median was 18 in both samples), even though differences exist in regard to the mean."
preferences for specific body parts: the eyes. Montoya asked 56 men and 82 women to rate 21 different body parts on a scale of 1 to 5. They found that men and women rated the eyes similarly, with an average rating of about 3.77 +- 1.23 (M+- SD). assuming these data are normally distributed a. what percentage of participants rated the eyes at least a 5 b. what percentage rated the eyes at most a 1
(A) p= .1587 (B) p= .0122
State whether each of the following statements is true or false. If false, then explain what would make the statement true. The central limit theorem explains why the mean is always at the center of a distribution. The standard error of the mean is the standard deviation of a sampling distribution of sample means. The mean of a sampling distribution is equal to the population mean from which samples are selected.
(a) False. The central limit theorem explains that regardless of the distribution of scores in a population, the sampling distribution of sample means selected at random from that population will approach the shape of a normal distribution, as the number of samples in the sampling distribution increases. (b) True. (c) True.
Suppose the researcher selects a sample of eight students from the population in Question 11. The sample consists of persons A, B, C, F, G, H, I, and J. What is the range of data in this sample? What is the IQR of data in this sample? What is the SIQR of data in this sample? What is the sample variance? What is the sample standard deviation?
(a) Range = 98 − 77 = 21. (b) IQR = 96 − 85 = 11. (c) SIQR = 5.5. (d) s2 = 55.41. (e) SD = 7.44.
state whether the first area is bigger, the second area is bigger, or the 2 areas are equal in each of the following situations: a. the area to the left of z=1.00 and the area to the right of z=-1.00 b. the area to the left of z=1.00 and the area to the left of z=-1.00 c. the area between the mean and z=1.20 and the area to the right of z=0.80 d. the area to the left of the mean and the area between z= +- 1.00 e. the area to the right of z=1.65 and the area to the right of z= -1.65
(a) The areas are equal. (b) The first area is bigger. (c) The first area is bigger. (d) The second area is bigger. (e) The second area is bigger."
a behavioral scientist measures attention in a sample of 31 participants. to measure the variance of attention, she computes SS= 120 for this sample. A: what are the degrees of freedom for variance B: compute the variance and standard deviation
(a) df = 30. (b) s2=120/30=4.0 SD=square root of 4=2
The sample mean is an unbiased estimator of the population mean. What do we expect the sample mean to be equal to when the population mean is equal to: 1. µ = 8? (b) µ = 0? (c) µ = 20? 2. µ = ∞? (e) µ = −40? (f) µ = 0.03?
(a) µM = 8. (b) µM = 0. (c) µM = −20. (d) µM = ∞. (e) µM = −∞. (f) µM = .03."
A population is normally distributed with a mean of −30 and a standard deviation of 4. What is the mean of the sampling distribution (µM) for this population? If a sample of 16 participants is selected from this population, what is the standard error of the mean (σM)? Sketch the shape of this distribution with M ± 3 SEM."
(a) µM = −30. (b) σM=σM=4/ square root of 16=1.00. (c) Sketch of sampling distribution with M ± 3 SEM
A population is normally distributed with a mean of 56 and a standard deviation of 12. What is the mean of the sampling distribution (µM) for this population? If a sample of 36 participants is selected from this population, what is the standard error of the mean (σM)?
56, 2
a sample of 60 scores is distributed with SS= 240. what is the sample variance and sample standard deviation for this distribution?
s2=240/60−1=4.07 SD= square root of 4.07=2.02
can the mean of a sampling distribution be a negative value
yes it can. the mean can be any value between positive infinity and negative infinity
A researcher observed a rat respond for a food reward by pressing one of three levers in a cage. Pressing the lever to the right (R) produced no food reward, pressing the lever to the left (L) produced a single food pellet, and pressing the lever at the center (C) produced two food pellets. Because the center level produced the largest reward, the researcher hypothesized that the rat would press this lever most often. Each trial ended when the rat pressed a lever. The researcher recorded lever pressing for 30 trials: L, L, R, L, R, C, R, L, C, L, L, C, C, C, R, C, R, C, L, C, C, L, C, C, C, L, C, C, C, C Create an ungrouped frequency distribution for these data.Do these data support the hypothesis Explain.
L=9 C=16 R=5 yes, the rat did press the center lever the most
Convert the following histogram to a frequency polygon. Hint: You must plot the midpoints of each interval to distribute a frequency polygon.
M shape
a student computes a standard deviation of 12. will the variance differ if 12 is the value for a population versus a sample standard deviation?
No. In both cases, the variance is the square of the standard deviation. So the population and sample variance will be 122 = 144."
A social psychologist records the age (in years) that a sample of eight participants first experienced peer pressure. The recorded ages for the participants are 14, 20, 17, 16, 12, 16, 15, and 16. Compute the SS, the variance, and the standard deviation for this sample using the definitional and computational formulas.
SS= 37.50 s2=25.36 SD=2.31
what is the key distinction between grouped and ungrouped data?
grouped data are distributed in intervals; ungrouped data are not
Can a nominal variable be numeric? Explain.
Yes because you can code a categorical variable numerically. Ex. January could be 1 and February could be 2...etc.
how do the sample mean and population mean differ?
a population mean is the mean for a set of scores in an entire population, whereas the sample mean is the mean for a sample, or a subset of scores in a population
using the unit normal table find the proportion under the standard normal curve that lies to the left of each of the following: a= z= .50 b= z= -1.32 c= z= 0 d= z= -1.96 e= z= -0.10
a= .6915 b= .0934 c= .5000 d= .0250 e= .4602
state whether each of the following describes a study measuring a qualitative or quantitative variable. Time in seconds to memorize a list of words. number of students in a statistics class. weight in pounds of newborn infants. Sat scores among college students.
continuous discrete continuous discrete
what are the 2 types of variables that can be quantitative?
continuous and discrete
a researcher measures the height and income of participants and finds that taller men tend to earn greater incomes that do shorter men. What type of research design must the researcher have used in this example
correlational, there are 2 continuous dependent variables
what is the difference between data and a raw score
data describe a set of measurements (made up of raw scores); a raw score describes individual measurements
the median is an appropriate measure for describing what types of data?
data that are skewed and ordinal data
to determine whether a new sleeping pill was effective, adult insomniacs received a pill (either real or fake), and their sleeping times were subsequently measured (in minutes) during an overnight observation period. Identify the dependent variable in this study. Identify the independent variable in this study.
dependent: sleeping times (min) independent: real/fake pill
is a pie chart typically used to summarize continuous or discrete/categorical data?
discrete/categorical data
state 3 commonly used research methods in behavior science
experimental, quasi-experimental, and correlational research methods
what is central tendency
measures of central tendency are statistical measures used to locate a single score that is most representative or descriptive of all scores in a distribution
A local high school is interested in studying how teacher perceptions of students, as being intelligent or not, affect the success of freshman students in the classroom. The school creates an Excel spreadsheet listing all freshman students in alphabetical order and places their names into one of two columns. All students listed in the second column are selected to participate in this study. is this sample design an example of random sampling? Explain.
no, because each student is not selected at random, and each students name is not replaced before selecting another student
A statistics instructor wants to measure the effectiveness of his teaching skills in a class of 102 students (N = 102). He selects students by waiting at the door to the classroom prior to his lecture and pulling aside every third student to give him or her a questionnaire. Is this sample design an example of random sampling? Explain. Assuming that all students attend his class that day, how many students will he select to complete the questionnaire?
no, because the students did not have an equal chance of being selected and therefore were not randomly selected. 34
a researcher measured behavior among all individuals in a small population. are inferential statistics necessary to draw conclusion concerning this population?
no, if the population is already known, you do not need to make inferences about it
Using the central limit theorem, what is the distribution of sample means when the population distribution is rectangle, normal, positively skewed, nonmodal, multimodal, negatively skewed,
normal
state the 4 scales of measurement. Which scale of measurement is the most informative?
normal, ordinal, interval, and ratio. ratio is the most informative
explain how conditional probabilities are related to sampling without replacement
sampling without replacement and conditional probabilities are related in that when we sample without replacement, the probability of each selection is conditional or dependent on the person or item that was selected in the previous selection
what re 2 steps to locate the cutoff score of a given proportion
step 1: locate the z score associated with a given proportion in the unit normal table step 2: transform the z score into a raw score (x)
define the central limit theorem
the central limit theorem states that regardless of the distribution of scores in a population, the sampling distribution of sample means selected from that population will be approximately normal
what are the values of the mean and the standard deviation in the standard normal distribution
the mean = 0, and the standard deviation = 1
A colleague measures the following heights (in inches) of 10 CEOs selected at random: 72, 75, 75, 66, 64, 79, 79, 75, 70, and 72. Which measure of central tendency is most appropriate for describing these data? Hint: Draw the shape of this distribution first
the median because the data are normally distributed, and the duration is a ratio scale measure
what type of distribution is most commonly applied to behavioral research
the normal distribution
what does the standard deviation measure
the standard deviation measures the average distance that scores deviate from their mean
how would the standard error change if (a) the population standard deviation increased and (b) the sample size increased
the standard error would increase. the standard error would decrease
state the standard normal transformation formula in words
the standard normal transformation is the difference between a score and the mean, divided by the standard deviation
The lower boundaries for the number of tattoos among prison inmates are 1, 4, 7, 10, 13, and 16. List the value for each upper boundary in this distribution.
the upper boundaries are 3,6,9,12,15,18
why is variance, as a measure of variability, preferred to the range, the IQR, and the SIQR
the variance is preferred because it includes all scores to estimate variability
what does it mean to say that the sample variance is unbiased
the variance of the sample will equal the variance of the population from which the sample was selected, on average
what values do you know to compute the formula for standard error
to compute standard error, you need to know the population standard deviation and the sample size
the upper boundary of one interval and the lower boundary of the next interval do not overlap in a simple frequency distribution. why?
to ensure that a single score cannot be counted in more than one interval
State whether each of the following statements concerning the sample mean is true or false. If false, then explain what would make the statement true. The value of the sample mean equals the population mean on average. The value of the sample mean can vary from sample to sample. There is more than a 5% probability of selecting a sample mean that is farther than 2 SEM from the population mean. The sampling distribution of sample means is approximately normally distributed.
true, true, false, true
frequency data are not always distributed in intervals. what types of data are not distributed in intervals?
ungrouped data sets with only a few different scores, and qualitative or categorical variables
distinguishing between sampling where order matters and sampling where order does not matter
when order matters, each time we select participants in a different order, it is counted as a different possible sample. When order doesn't matter, selecting participants in a different order is counted as the same sample